Bethe-Salpeter Approach for the $P_{33}$ Elastic Pion-Nucleon Scattering in Heavy Baryon Chiral Perturbation Theory

Abstract

Heavy Baryon Chiral Perturbation Theory (HBChPT) to leading order provides a kernel to solve the Bethe-Salpeter equation for the $P_{33}$ ($\Delta (1232)$-channel) $\pi -N$ system, in the infinite nucleon mass limit. Crossed Born terms include, when iterated within the Bethe-Salpeter equation, both {\it all} one- and {\it some} two-pion intermediate states, hence preserving elastic unitarity below the two-pion production threshold. This suggests searching for a solution with the help of dispersion relations and suitable subtraction constants, when all in-elasticities are explicitly neglected. The solution allows for a successful description of the experimental phase shift from threshold up to $\sqrt{s}=1500$ MeV in terms of four subtraction constants. Next-to-leading order HBChPT calculations are also used to estimate the unknown subtraction constants which appear in the solution. Large discrepancies are encountered which can be traced to the slow convergence rate of HBChPT.

11 pages, 3 figures

References in corpus (4)

• Pion-nucleon scattering in chiral perturbation theory II: Fourth order calculation
• Chiral unitary meson-baryon dynamics in the presence of resonances: Elastic pion-nucleon scattering
• Improved Unitarized Heavy Baryon Chiral Perturbation Theory for $\pi N$ Scattering
• Unitarized pion-nucleon scattering within Heavy Baryon Chiral Perturbation Theory

Cited by in corpus (17)

• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• On meson resonances and chiral symmetry
• $S=-1$ Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory and the $S_{01}-$ $\Lambda$(1405) and $-\Lambda$(1670) Resonances
• On baryon resonances and chiral symmetry
• The $S_{11}-N$(1535) and $-N$(1650) Resonances in Meson-Baryon Unitarized Coupled Channel Chiral Perturbation Theory
• Dynamically generated open charmed baryons beyond the zero range approximation
• On charm baryon resonances and chiral symmetry
• D-wave baryon resonances with charm from coupled-channel dynamics
• Thermal rho and sigma mesons from chiral symmetry and unitarity
• Low-lying even parity meson resonances and spin-flavor symmetry
• πN scattering in relativistic baryon chiral perturbation theory revisited
• Open charm meson in nuclear matter at finite temperature beyond the zero range approximation
• Off-shell effects on the interaction of Nambu-Goldstone bosons and $D$ mesons
• Improved Unitarized Heavy Baryon Chiral Perturbation Theory for pion-nucleon Scattering to fourth order
• Unitarized chiral perturbation theory of hadrons
• S=--1 Meson-Baryon Scattering in Coupled Channel Unitarized Chiral Perturbation Theory